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3 years ago

In ΔEFG, the measure of ∠G=90°, FG = 1.5 feet, and EF = 7.5 feet. Find the measure of ∠F to the nearest degree.

Mathematics

2 answers:

fomenos3 years ago

8 0

Answer:

78°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relations between angles and sides of a right triangle. In particular, ...

Cos = Adjacent/Hypotenuse

cos(F) = FG/FE = 1.5/7.5 = 0.2

The inverse cosine function is used to find the angle:

∠F = arccos(0.2)

∠F ≈ 78°

Artemon [7]3 years ago

8 0

Answer:

Step-by-step explanation:

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AveGali [126]

Some basic formulas involving triangles

\ a^2 = b^2 + c^2 - 2bc \textrm{ cos } \alphaa 2 =b 2+2 + c 2

−2bc cos α

\ b^2 = a^2 + c^2 - 2ac \textrm{ cos } \betab 2=

m_b^2 = \frac{1}{4}( 2a^2 + 2c^2 - b^2 )m b2 = 41(2a 2 + 2c 2-b 2)

Bisector formulas

\ \frac{a}{b} = \frac{m}{n} ba =nm

\ l^2 = ab - mnl 2=ab-mm

A = \frac{1}{2}a\cdot b = \frac{1}{2}c\cdot hA=

\ A = \sqrt{p(p - a)(p - b)(p - c)}A=

p(p−a)(p−b)(p−c)

\iits whatever A = prA=pr with r we denote the radius of the triangle inscribed circle

\ A = \frac{abc}{4R}A=

abc

- R is the radius of the prescribed circle

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3 years ago

The service life of a battery used in a cardiac pacemaker is assumed to be normally distributed. A random sample of ten batterie

Fittoniya [83]

Answer:

The confidence interval is $25.16 < \mu < 26.85$

Step-by-step explanation:

From the question we are given a data set

25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.

The mean of the this sample data is

$\= x = \frac{\sum x_i}{n}$

where is the sample size with values n = 10

$\= x = \frac{25.5+ 26.1+ 26.8+23.2+ 24.2+ 28.4+ 25.0+ 27.8+ 27.3+ 25.7}{10}$

$\= x = 26$

The standard deviation is evaluated as

$\sigma = \sqrt{\frac{\sum (x-\= x)}{n} }$

substituting values

$= \sqrt{\frac{ ( 25.5-26)^2, (26.1-26)^2, (26.8-26)^2, (23.2-26)^2}{10} }$

$\cdot \ \cdot \ \cdot \sqrt{\frac{ ( 24.2-26)^2, (28.4-26)^2+( 25.0-26)^2+ (27.8-26)^2+( 27.3-26)^2+( 25.7-26)^2}{10} }$

$\sigma = 1.625$

The confidence level is given as 90% hence the level of significance is calculated as

$\alpha = 100 -90$

$\alpha =10$ %

$\alpha = 0.10$

Now the critical values of $\frac{\alpha }{2}$ is obtained from the normal distribution table as

$Z_{\frac{\alpha }{2} } = 1.645$

The reason we are obtaining the critical values of $\frac{\alpha }{2}$ instead of $\alpha$ is because we are considering two tails of the area under the normal curve

The margin of error is evaluated as

$MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

substituting values

$MOE = 1.645 * \frac{1.625 }{\sqrt{10} }$

$MOE = 0.845$

The 90%, two sided confidence interval is mathematically evaluated as

$\= x - MOE < \mu < \= x + MOE$

$26 - 0.845 < \mu < 26 + 0.845$

$25.16 < \mu < 26.85$

Given that the lower and the upper limit is greater than 25 then we can assure the manufactures that the battery life exceeds 25 hours

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3 years ago